Each trig function has a “co-” partner: sine and cosine, tangent and cotangent, secant and cosecant. In a right triangle the two acute angles add up to 90°, so the sine of one is the cosine of the other – that is where the “co” (complement) comes from.
How to use the Cofunction Calculator
- Function
- Angle θ (degrees)
Everything is calculated in your browser, so results appear instantly and nothing you type is sent to a server.
How it works
Choose the function and enter θ in degrees. The calculator swaps the function for its cofunction and the angle for its complement 90° − θ, and evaluates both sides (with the exact value for multiples of 15°).
Tips
- Check whether your angle is in degrees or radians – the unit menu converts for you.
- Use the unit circle to predict the sign of each function in each quadrant.
- Inverse functions return a principal value; other angles may have the same sine or cosine.
- Keep exact values such as √3/2 when an angle is a multiple of 15°.
Common mistakes to avoid
- Using degree values in a calculator set to radians (or the reverse).
- Forgetting that tan and sec are undefined at 90° and 270°.
- Writing sin⁻¹(x) as 1/sin(x) – it is the inverse function, not the reciprocal.
Formula
sin(90° − θ) = cos θ, tan(90° − θ) = cot θ, sec(90° − θ) = csc θ (and the reverse)Worked example
Inputs — Function: sin; Angle θ (degrees): 30.
Results — Cofunction form = sin(30°) = cos(60°); Value = 1/2 ≈ 0.5; Identity used = sin(90° − θ) = cos(θ).
Key terms
- Complementary angles
- Two angles adding up to 90°.
Frequently asked questions
What are cofunctions?
Pairs of functions equal at complementary angles: sin/cos, tan/cot, sec/csc.
Why is sin 30° = cos 60°?
30° and 60° are the two acute angles of the same right triangle.
Does it work in radians?
Yes, with π/2 − θ in place of 90° − θ.
Do cofunction identities hold for angles above 90°?
Yes – they hold for every angle.
What formula does the Cofunction Calculator use?
sin(90° − θ) = cos θ, tan(90° − θ) = cot θ, sec(90° − θ) = csc θ (and the reverse).